सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

39 have seen above that the first term is no other than the Mean Sun ignoring the integral number. Verses 10, 11. Proof of other methods of computing planetary position. Even as the sums or differences of two or more of the numbers of Adhimāsas, Kshayāhas, lunations etc give the number of sidereal revolutions of the planets the sums or differences of two or more of the posi- tions of the imaginary planets which go by the names Adhimāsa-graha, Kshayāhagraha etc computed out of the numbers of those Adhimāsas Kshayāhas etc. give the respective planetary positions. Comm. This interesting concept is based upon the following principle. Suppose P to be the number of side- real revolutions of a planet; then (A × P) / M gives the planetary position, where A is the Ahargaṇa, and M the number of mean solar days in a Kalpa. Now suppose P = x ± y ± z where x, y, z are the numbers of Adhimāsās etc in a Kalpa, then (A × P) / M = (A × x) / M ± (A × y) / M ± (A × z) / M • The terms on the right-hand-side may be construed to be the Adhimāsa-graha etc, which are the positions of imaginary planets and their sums or differences give there- fore the position of the planet, as could be seen from the above equation. Thus for example, we have the equation P₁ — 13P₂ = a where P₁ is the number of the sidereal revolutions of the Moon and P₂ the number of the sidereal revolutions of the Sun, a stands for the Adhimāsas because Chāndramāsas — Sauramāsas = Adhimāsas; but Chāndra- māsas = P₁ — P₂ and Sauramāsas = 12 P₂ so that P₁ — P₂ — 12P₂ = a ie P₁ — 13P₂ = a. From this equation P₁ = a + 13P₂ ∴ (A × P₁) / M = (a × A) / M + (13P₂ × A) / M •